If the full angle is cut in half - as shown with the blue angle η at figure 2 - we get an isosceles triangle (green) where the angles φ and τ are equal. The figures show a circle with a central angle describing an arc and we'll try to show that the yellow angles ε and σ are exactly one quarter of the cyan central angle θ. But why is the bulge 1/4 of the included angle and where does the tangent fit in? There are many ways to explain this. Now you have a bulge value for the arc segment in the polyline, and you can try out the formula above. Drop the endpoint somewhere, leave the polyline command and type this at the command line: Command: (setq ent (entget (entlast))) Start drawing a lightweight polyline, type "A" for arc, then "A" again for Angle and "120.0" for the included angle. So, a bulge of 0.57735 is describing an included angle of 2.09439 radians (which is 120.0 degrees, by the way).
Simply use the built-in function ATAN to getĪn angle and multiply it by 4 in order to get the included angle: (* 4.0 (atan 0.57735)) In fact, once you have a bulge value, you can very quickly retrieve the included angle by inverting the above statement. Well, it also says that the bulge has something to do with the tangent of a quarter of the included angle of an arc. It says that the only information given for arc segments in polylines are two vertices and a bulge. What does this mean and how can an arc be defined without even knowing the radius - or at least a chord length? A bulge of 0 indicates a straight segment, and a bulge of 1 is a semicircle. A negative bulge value indicates that the arc goes clockwise from the selected vertex to the next vertex. The bulge is the tangent of 1/4 of the included angle for the arc between the selected vertex and the next vertex in the polyline's vertex list. So, what is a bulge for a circular arc and how is it defined? In AutoCAD's online help reference, it says about bulges for polylines: Both figures includes all of the attributes above, but for doing calculations with bulges, we'll mostly use the piece of pie that the arc cuts out of a circle, the circular sector. This line is drawn from the midpoint of an arc and perpendicular to its chord.Įxcept for the arc itself, an arc can describe two distinct geometric forms: Circular segment and circular sector.
This line starts at the center and is perpendicular to the chord. Given two fixed vertices, there is also a specific midpoint (P3) of an arc.An infinite amount of chords can be described by both circles and arcs, but for an arc there is only one distinct chord that passes through its vertices (for a circle, there is only one distinct chord that passes through the center, the diameter, but it doesn't describe any specific vertices). vertices (although sometimes it is practical to talk about specific points that a circle passes through, there are no distinct vertices on the circumference of a circle). Start point and end point (P1 and P2) a.k.a.The arc length is equal to the perimeter in a full circle.Īdding to these attributes are some that are specific for an arc: Center point (P) is also the same as in the circle.Radius (r) is the same as in the circle the arc is a portion of.This article only deals with polyline bulges, and because polyline bulges are describing circular arcs, let's first look at the geometry of a circular arc.īecause a circular arc describes a portion of the circumference of a circle, it has all the attributes of a circle: In AutoCAD, bulges are used in shapes and in arc segments of polylines. In other words: bulges are all about curvature. Which is the time they tend to develop bulges in not so strategic places. Bulges are something that women have (mostly to please the opposite sex it seems) and something that guys try to get by placing socks in strategic places.
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